Inverse function?

Question

f(x)= 3x-2
--------
x+7

Find the inverse function of f and show they are inverses.
the 3x-2 is over the x+7, I just didn't know how to put it into the computer any other way. Please show work.

Answer 1

Change f(x) to y:

y = (3x-2)/(x+7)

Swap all x's with y's and y's with x's:

x = (3y-2)/(y+7)

Solve for y:

x(y+7) = 3y-2
xy + 7x = 3y-2
xy - 3y = -2 - 7x
y(x-3) = -2 - 7x
y = (-2 - 7x)/(x-3) = (2+7x)/(3-x)

So the inverse would be: (2+7x)/(3-x)

Answer 2

So, you have a function which, when you feed it a value for x, gives you a value based on the equation.

e.g., f(0) = -2/7

You need another function (call it g) such that if you give it the answer, it will give you the initial value of x.

e.g., g(-2/7) = 0

Sounds like a simple "solve for x" problem.

Start with your f(x) = (3x-2)/(x+7) and treat f(x) as a variable. You are trying to isolate x to end up with an equation of the shape:

x = g(f(x))
meaning: x is a function that contains only f(x) as its variable.

Answer 3

Let y=(3x-2)/(x+7)..............(i)

=>xy + 7y=3x-2
=>x(3-y)=7y + 2
=>x=(7y+2)/(3-y)

=>f inverse of x is is=(7x+2)/(3-x)

If they are inverse of each other then f(f^-1(x))=x which mean that we have to put x=(7x+2)/(3-x) in the original equation(i)
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Thus,
[3(7x+2)/(3-x) - 2]/[(7x+2)/(3-x)+7]

=>[(21x + 6 - 6 + 2x)/(3-x)]/[(7x+2+21-7x)/(3-x)]
=>[23x]/[23]=x
=>We have calculated correct!

Answer 4

Let y=(3x-2)/(x+7).
So, yx+7y=3x-2.
Now, yx-3x=-2-7y.
Or, x(y-3)=-2-7y.
So, x=(-2-7y)/(y-3)=(2+7y)/(3-y).

So, the inverse f-1(x) is (2+7x)/(3-x).

Answer 5

You could type it in like this:

f(x) = (3x-2)/(x+7)

Now you know how to write it; next, learn to do your own homework, or your schooling will be pointless.